pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
debugmsg("pseries ctor from ex,epvector", LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(is_ex_exactly_of_type(rel_, relational));
- GINAC_ASSERT(is_ex_exactly_of_type(rel_.lhs(),symbol));
+ GINAC_ASSERT(is_exactly_a<relational>(rel_));
+ GINAC_ASSERT(is_exactly_a<symbol>(rel_.lhs()));
point = rel_.rhs();
- var = *static_cast<symbol *>(rel_.lhs().bp);
+ var = rel_.lhs();
}
DEFAULT_UNARCHIVE(pseries)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
void pseries::print(const print_context & c, unsigned level) const
int pseries::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, pseries));
+ GINAC_ASSERT(is_a<pseries>(other));
const pseries &o = static_cast<const pseries &>(other);
// first compare the lengths of the series...
if (var.is_equal(s)) {
// Return last exponent
if (seq.size())
- return ex_to<numeric>((*(seq.end() - 1)).coeff).to_int();
+ return ex_to<numeric>((seq.end()-1)->coeff).to_int();
else
return 0;
} else {
if (var.is_equal(s)) {
// Return first exponent
if (seq.size())
- return ex_to<numeric>((*(seq.begin())).coeff).to_int();
+ return ex_to<numeric>((seq.begin())->coeff).to_int();
else
return 0;
} else {
int lo = 0, hi = seq.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
- GINAC_ASSERT(is_ex_exactly_of_type(seq[mid].coeff, numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(seq[mid].coeff));
int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
switch (cmp) {
case -1:
return *this;
}
-/** Evaluate coefficients. */
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
ex pseries::eval(int level) const
{
if (level == 1)
++i;
}
return (new pseries(relational(var,point), newseq))
- ->setflag(status_flags::dynallocated | status_flags::expanded);
+ ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
/** Implementation of ex::diff() for a power series. It treats the series as a
ex basic::series(const relational & r, int order, unsigned options) const
{
epvector seq;
- numeric fac(1);
+ numeric fac = 1;
ex deriv = *this;
ex coeff = deriv.subs(r);
- const symbol &s = static_cast<symbol &>(*r.lhs().bp);
+ const symbol &s = ex_to<symbol>(r.lhs());
if (!coeff.is_zero())
seq.push_back(expair(coeff, _ex0()));
int n;
for (n=1; n<order; ++n) {
- fac = fac.mul(numeric(n));
+ fac = fac.mul(n);
+ // We need to test for zero in order to see if the series terminates.
+ // The problem is that there is no such thing as a perfect test for
+ // zero. Expanding the term occasionally helps a little...
deriv = deriv.diff(s).expand();
- if (deriv.is_zero()) {
- // Series terminates
+ if (deriv.is_zero()) // Series terminates
return pseries(r, seq);
- }
+
coeff = deriv.subs(r);
if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, numeric(n)));
+ seq.push_back(expair(fac.inverse() * coeff, n));
}
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1()), numeric(n)));
+ seq.push_back(expair(Order(_ex1()), n));
return pseries(r, seq);
}
{
epvector seq;
const ex point = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- ex s = r.lhs();
-
- if (this->is_equal(*s.bp)) {
+ GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+
+ if (this->is_equal_same_type(ex_to<symbol>(r.lhs()))) {
if (order > 0 && !point.is_zero())
seq.push_back(expair(point, _ex0()));
if (order > 1)
// Series multiplication
epvector new_seq;
-
int a_max = degree(var);
int b_max = other.degree(var);
int a_min = ldegree(var);
* @see ex::series */
ex mul::series(const relational & r, int order, unsigned options) const
{
- ex acc; // Series accumulator
-
- // Get first term from overall_coeff
- acc = overall_coeff.series(r, order, options);
-
+ pseries acc; // Series accumulator
+
// Multiply with remaining terms
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- for (; it!=itend; ++it) {
- ex op = it->rest;
- if (op.info(info_flags::numeric)) {
- // series * const (special case, faster)
- ex f = power(op, it->coeff);
- acc = ex_to<pseries>(acc).mul_const(ex_to<numeric>(f));
- continue;
- } else if (!is_ex_exactly_of_type(op, pseries))
- op = op.series(r, order, options);
- if (!it->coeff.is_equal(_ex1()))
- op = ex_to<pseries>(op).power_const(ex_to<numeric>(it->coeff), order);
+ const epvector::const_iterator itbeg = seq.begin();
+ const epvector::const_iterator itend = seq.end();
+ for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
+ ex op = recombine_pair_to_ex(*it).series(r, order, options);
// Series multiplication
- acc = ex_to<pseries>(acc).mul_series(ex_to<pseries>(op));
+ if (it==itbeg)
+ acc = ex_to<pseries>(op);
+ else
+ acc = ex_to<pseries>(acc.mul_series(ex_to<pseries>(op)));
}
- return acc;
+ return acc.mul_const(ex_to<numeric>(overall_coeff));
}
ex pseries::power_const(const numeric &p, int deg) const
{
// method:
+ // (due to Leonhard Euler)
// let A(x) be this series and for the time being let it start with a
// constant (later we'll generalize):
// A(x) = a_0 + a_1*x + a_2*x^2 + ...
// then of course x^(p*m) but the recurrence formula still holds.
if (seq.empty()) {
- // as a spacial case, handle the empty (zero) series honoring the
+ // as a special case, handle the empty (zero) series honoring the
// usual power laws such as implemented in power::eval()
if (p.real().is_zero())
- throw (std::domain_error("pseries::power_const(): pow(0,I) is undefined"));
+ throw std::domain_error("pseries::power_const(): pow(0,I) is undefined");
else if (p.real().is_negative())
- throw (pole_error("pseries::power_const(): division by zero",1));
+ throw pole_error("pseries::power_const(): division by zero",1);
else
return *this;
}
- int ldeg = ldegree(var);
+ const int ldeg = ldegree(var);
+ if (!(p*ldeg).is_integer())
+ throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+
+ // O(x^n)^(-m) is undefined
+ if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative())
+ throw pole_error("pseries::power_const(): division by zero",1);
// Compute coefficients of the powered series
exvector co;
}
if (!sum.is_zero())
all_sums_zero = false;
- co.push_back(sum / coeff(var, ldeg) / numeric(i));
+ co.push_back(sum / coeff(var, ldeg) / i);
}
// Construct new series (of non-zero coefficients)
bool higher_order = false;
for (int i=0; i<deg; ++i) {
if (!co[i].is_zero())
- new_seq.push_back(expair(co[i], numeric(i) + p * ldeg));
+ new_seq.push_back(expair(co[i], p * ldeg + i));
if (is_order_function(co[i])) {
higher_order = true;
break;
}
}
if (!higher_order && !all_sums_zero)
- new_seq.push_back(expair(Order(_ex1()), numeric(deg) + p * ldeg));
+ new_seq.push_back(expair(Order(_ex1()), p * ldeg + deg));
return pseries(relational(var,point), new_seq);
}
* @see ex::series */
ex power::series(const relational & r, int order, unsigned options) const
{
- ex e;
- if (!is_ex_exactly_of_type(basis, pseries)) {
- // Basis is not a series, may there be a singularity?
- bool must_expand_basis = false;
- try {
- basis.subs(r);
- } catch (pole_error) {
- must_expand_basis = true;
- }
-
- // Is the expression of type something^(-int)?
- if (!must_expand_basis && !exponent.info(info_flags::negint))
- return basic::series(r, order, options);
+ // If basis is already a series, just power it
+ if (is_ex_exactly_of_type(basis, pseries))
+ return ex_to<pseries>(basis).power_const(ex_to<numeric>(exponent), order);
+
+ // Basis is not a series, may there be a singularity?
+ bool must_expand_basis = false;
+ try {
+ basis.subs(r);
+ } catch (pole_error) {
+ must_expand_basis = true;
+ }
- // Is the expression of type 0^something?
- if (!must_expand_basis && !basis.subs(r).is_zero())
- return basic::series(r, order, options);
+ // Is the expression of type something^(-int)?
+ if (!must_expand_basis && !exponent.info(info_flags::negint))
+ return basic::series(r, order, options);
- // Singularity encountered, expand basis into series
- e = basis.series(r, order, options);
- } else {
- // Basis is a series
- e = basis;
+ // Is the expression of type 0^something?
+ if (!must_expand_basis && !basis.subs(r).is_zero())
+ return basic::series(r, order, options);
+
+ // Singularity encountered, is the basis equal to (var - point)?
+ if (basis.is_equal(r.lhs() - r.rhs())) {
+ epvector new_seq;
+ if (ex_to<numeric>(exponent).to_int() < order)
+ new_seq.push_back(expair(_ex1(), exponent));
+ else
+ new_seq.push_back(expair(Order(_ex1()), exponent));
+ return pseries(r, new_seq);
}
-
- // Power e
+
+ // No, expand basis into series
+ ex e = basis.series(r, order, options);
return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
}
ex pseries::series(const relational & r, int order, unsigned options) const
{
const ex p = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol &s = static_cast<symbol &>(*r.lhs().bp);
+ GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+ const symbol &s = ex_to<symbol>(r.lhs());
if (var.is_equal(s) && point.is_equal(p)) {
if (order > degree(s))
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